Secret sharing is a process by which secrets are distributed among an arbitrary number of servers. A concern in secret sharing is the possibility of an adversary who may corrupt a fixed portion of the servers. When the adversary corrupts a server, it learns all information stored on that server. The adversary can force corrupt servers to behave arbitrarily, irrespective of the protocol. Thus, it is imperative to implement a secure secret sharing protocol.
As such, a number of researchers have devised various mobile secret sharing protocols. For example, a mobile secret sharing protocol was described by David Schultz in “Mobile Proactive Secret Sharing,” PhD thesis, Massachusetts Institute of Technology, 2007, which is hereby incorporated by reference as though fully set forth herein. In Schultz' thesis, the threshold of corruption is lowered by employing “virtual servers” and having each real server keep these virtual servers' shares in memory. As admitted by Shultz, “[t]his approach is somewhat unsatisfying theoretically because using this method to reduce the threshold does not reduce the asymptotic computational overhead of the protocol.”
Thus, a continuing need exists for a mobile proactive secret sharing protocol that allows for the number of servers used in the computation to decrease without relying on virtual servers to engage in the protocol.